Essential characteristics of noise

Why does
photonic noise variance have to be proportional to the signal?

It is worth
noting that photonic noise is due to the light signal itself and is independent
of the camera. It is mathematically modeled by a Poisson process, and
consequently, the mean signal is equal to its variance. (This is a mathematical
property of a Poisson process.) It is possible to prove this property without
any assumptions; however:

Assume that a
pixel receives photons
and has a noise standard deviation . Let’snow cut this pixel into four
smaller pixels of equal size. Each small pixel receives an average number of
photons and
has a noise standard deviation . Since the variance is additive, the
variance of the large pixel value is the sum of the variances of the small
pixel values. Thus:

From this, it
is not very difficult to see that has to be proportional to .

Photonic
noise is the main source of noise in the midtones, and follows the rule of 3dB
per EV:

An object reflecting light twice as much as another one has a better SNR
(+3dB).

Doubling the exposure time improves the SNR by 3dB.

A camera with the same field of view and twice as many pixels as another camera
has a lower SNR (-3dB). Indeed, each pixel receives two times less light in the
high-resolution camera as in the low-resolution camera. However, the high resolution
camera contains more detail, and can still be converted into a low-resolution
camera by carefully-performed sub-sampling. In this case, the noise level is
the same (see “Noise Normalization”).